Since the subject of definitions arose, I am curious abouthow and what users of this list tell their students aboutthe real numbers. I have been teaching real analysis a few times in recent years, and spend a lot of time on thereals, since constructing them lays an excellent groundworkfor the whole concept of delta-epsilon stuff. I use anapproach developed by Gabe Stolzenberg which defines realsas families of intervals of rational numbers. It combines,it seems to me, the best features of both the Dedekind and Cauchy approaches. I'd very much like to hear whatothers are doing.